/* * ECOS - Embedded Conic Solver. * Copyright (C) 2012-2015 A. Domahidi [domahidi@embotech.com], * Automatic Control Lab, ETH Zurich & embotech GmbH, Zurich, Switzerland. * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program. If not, see . */ #ifndef __ECOS_H__ #define __ECOS_H__ #ifdef __cplusplus extern "C" { #endif #include "glblopts.h" #include "spla.h" #include "cone.h" #include "kkt.h" #if PROFILING > 0 #include "timer.h" #endif #if CTRLC > 0 #include "ctrlc.h" #endif /* ECOS VERSION NUMBER - FORMAT: X.Y.Z --------------------------------- */ #define ECOS_VERSION ("2.0.8") /* DEFAULT SOLVER PARAMETERS AND SETTINGS STRUCT ----------------------- */ #define MAXIT (100) /* maximum number of iterations */ #define FEASTOL (1E-8) /* primal/dual infeasibility tolerance */ #define ABSTOL (1E-8) /* absolute tolerance on duality gap */ #define RELTOL (1E-8) /* relative tolerance on duality gap */ #define FTOL_INACC (1E-4) /* inaccurate solution feasibility tol. */ #define ATOL_INACC (5E-5) /* inaccurate solution absolute tol. */ #define RTOL_INACC (5E-5) /* inaccurate solution relative tol. */ #define GAMMA (0.99) /* scaling the final step length */ #define STATICREG (1) /* static regularization: 0:off, 1:on */ #define DELTASTAT (7E-8) /* regularization parameter */ #define DELTA (2E-7) /* dyn. regularization parameter */ #define EPS (1E-13) /* dyn. regularization threshold (do not 0!) */ #define VERBOSE (1) /* bool for verbosity; PRINTLEVEL < 3 */ #define NITREF (9) /* number of iterative refinement steps */ #define IRERRFACT (6) /* factor by which IR should reduce err */ #define LINSYSACC (1E-14) /* rel. accuracy of search direction */ #define SIGMAMIN (1E-4) /* always do some centering */ #define SIGMAMAX (1.0) /* never fully center */ #define STEPMIN (1E-6) /* smallest step that we do take */ #define STEPMAX (0.999) /* largest step allowed, also in affine dir. */ #define SAFEGUARD (500) /* Maximum increase in PRES before ECOS_NUMERICS is thrown. */ /*Ecos exponential cone default settings*/ #ifdef EXPCONE #define MAX_BK (90) /*Maximum backtracking steps*/ #define BK_SCALE (0.8) /*Backtracking constant*/ #define MIN_DISTANCE (0.1) /* dont let sqrt(r), sqrt(-u) or sqrt(v) become smaller than MIN_DISTANCE*mu*/ #define CENTRALITY (1) /*Centrality requirement*/ #endif /* EQUILIBRATION METHOD ------------------------------------------------ */ #define EQUILIBRATE (1) /* use equlibration of data matrices? >0: yes */ #define EQUIL_ITERS (3) /* number of equilibration iterations */ #define RUIZ_EQUIL /* define algorithm to use - if both are ... */ /*#define ALTERNATING_EQUIL*/ /* ... commented out no equlibration is used */ /* EXITCODES ----------------------------------------------------------- */ #define ECOS_OPTIMAL (0) /* Problem solved to optimality */ #define ECOS_PINF (1) /* Found certificate of primal infeasibility */ #define ECOS_DINF (2) /* Found certificate of dual infeasibility */ #define ECOS_INACC_OFFSET (10) /* Offset exitflag at inaccurate results */ #define ECOS_MAXIT (-1) /* Maximum number of iterations reached */ #define ECOS_NUMERICS (-2) /* Search direction unreliable */ #define ECOS_OUTCONE (-3) /* s or z got outside the cone, numerics? */ #define ECOS_SIGINT (-4) /* solver interrupted by a signal/ctrl-c */ #define ECOS_FATAL (-7) /* Unknown problem in solver */ /* SETTINGS STRUCT ----------------------------------------------------- */ typedef struct settings{ pfloat gamma; /* scaling the final step length */ pfloat delta; /* regularization parameter */ pfloat eps; /* regularization threshold */ pfloat feastol; /* primal/dual infeasibility tolerance */ pfloat abstol; /* absolute tolerance on duality gap */ pfloat reltol; /* relative tolerance on duality gap */ pfloat feastol_inacc; /* primal/dual infeasibility relaxed tolerance */ pfloat abstol_inacc; /* absolute relaxed tolerance on duality gap */ pfloat reltol_inacc; /* relative relaxed tolerance on duality gap */ idxint nitref; /* number of iterative refinement steps */ idxint maxit; /* maximum number of iterations */ idxint verbose; /* verbosity bool for PRINTLEVEL < 3 */ #ifdef EXPCONE /*Exponential cone settings*/ idxint max_bk_iter; /* Maximum backtracking iterations */ pfloat bk_scale; /* Backtracking scaling */ pfloat centrality; /* Centrality bound, ignored when centrality vars = 0*/ #endif } settings; /* INFO STRUCT --------------------------------------------------------- */ typedef struct stats{ pfloat pcost; pfloat dcost; pfloat pres; pfloat dres; pfloat pinf; pfloat dinf; pfloat pinfres; pfloat dinfres; pfloat gap; pfloat relgap; pfloat sigma; pfloat mu; pfloat step; pfloat step_aff; pfloat kapovert; idxint iter; idxint nitref1; idxint nitref2; idxint nitref3; #if PROFILING > 0 pfloat tsetup; pfloat tsolve; #endif #if PROFILING > 1 pfloat tfactor; pfloat tkktsolve; pfloat torder; pfloat tkktcreate; pfloat ttranspose; pfloat tperm; pfloat tfactor_t1; pfloat tfactor_t2; #endif #ifdef EXPCONE /* Counters for backtracking, each of these counts * one condition that can fail and cause a backtrack */ idxint pob; /* Potential decreases */ idxint cb; /* Centrality violations */ idxint cob; /* The s'z of one cone is too small w.r.t. mu */ idxint pb; /* Primal infeasibility */ idxint db; /* Dual infeasibility */ idxint affBack; /* Total affine backtracking steps */ idxint cmbBack; /* Total combined backtracking steps */ pfloat centrality; /*Centrality at the end of the backtracking*/ #endif } stats; /* ALL DATA NEEDED BY SOLVER ------------------------------------------- */ typedef struct pwork{ /* dimensions */ idxint n; /* number of primal variables x */ idxint m; /* number of conically constrained variables s */ idxint p; /* number of equality constraints */ idxint D; /* degree of the cone */ /* variables */ pfloat* x; /* primal variables */ pfloat* y; /* multipliers for equality constaints */ pfloat* z; /* multipliers for conic inequalities */ pfloat* s; /* slacks for conic inequalities */ pfloat* lambda; /* scaled variable */ pfloat kap; /* kappa (homogeneous embedding) */ pfloat tau; /* tau (homogeneous embedding) */ /* best iterate seen so far */ /* variables */ pfloat* best_x; /* primal variables */ pfloat* best_y; /* multipliers for equality constaints */ pfloat* best_z; /* multipliers for conic inequalities */ pfloat* best_s; /* slacks for conic inequalities */ pfloat best_kap; /* kappa (homogeneous embedding) */ pfloat best_tau; /* tau (homogeneous embedding) */ pfloat best_cx; pfloat best_by; pfloat best_hz; stats* best_info; /* info of best iterate */ /* temporary stuff holding search direction etc. */ pfloat* dsaff; pfloat* dzaff; pfloat* W_times_dzaff; pfloat* dsaff_by_W; pfloat* saff; pfloat* zaff; /* cone */ cone* C; /* problem data */ spmat* A; spmat* G; pfloat* c; pfloat* b; pfloat* h; /* indices that map entries of A and G to the KKT matrix */ idxint *AtoK; idxint *GtoK; #if defined EQUILIBRATE && EQUILIBRATE > 0 /* equilibration vector */ pfloat *xequil; pfloat *Aequil; pfloat *Gequil; #endif /* scalings of problem data */ pfloat resx0; pfloat resy0; pfloat resz0; /* residuals */ pfloat *rx; pfloat *ry; pfloat *rz; pfloat rt; pfloat hresx; pfloat hresy; pfloat hresz; /* norm iterates */ pfloat nx,ny,nz,ns; /* temporary storage */ pfloat cx; pfloat by; pfloat hz; pfloat sz; /* KKT System */ kkt* KKT; /* info struct */ stats* info; /* settings struct */ settings* stgs; } pwork; /* SOME USEFUL MACROS -------------------------------------------------- */ #define MAX(X,Y) ((X) < (Y) ? (Y) : (X)) /* maximum of 2 expressions */ /* safe division x/y where y is assumed to be positive! */ #define SAFEDIV_POS(X,Y) ( (Y) < EPS ? ((X)/EPS) : (X)/(Y) ) /* METHODS */ /* set up work space * could be done by codegen * * Parameters: * idxint n Number of variables * idxint m Number of inequalities, number of rows of G * idxint p Number of equality constraints * idxint l Dimension of positive orthant * idxint ncones Number of second order cones * idxint* q Array of length 'ncones', defines the dimension of each cone * idxint nex Number of exponential cones * pfloat* Gpr Sparse G matrix data array (column compressed storage) * idxint* Gjc Sparse G matrix column index array (column compressed storage) * idxint* Gir Sparse G matrix row index array (column compressed storage) * pfloat* Apr Sparse A matrix data array (column compressed storage) (can be all NULL if no equalities are present) * idxint* Ajc Sparse A matrix column index array (column compressed storage) (can be all NULL if no equalities are present) * idxint* Air Sparse A matrix row index array (column compressed storage) (can be all NULL if no equalities are present) * pfloat* c Array of size n, cost function weights * pfloat* h Array of size m, RHS vector of cone constraint * pfloat* b Array of size p, RHS vector of equalities (can be NULL if no equalities are present) */ pwork* ECOS_setup(idxint n, idxint m, idxint p, idxint l, idxint ncones, idxint* q, idxint nex, pfloat* Gpr, idxint* Gjc, idxint* Gir, pfloat* Apr, idxint* Ajc, idxint* Air, pfloat* c, pfloat* h, pfloat* b); #ifdef EXPCONE pfloat expConeLineSearch(pwork* w, pfloat dtau, pfloat dkappa, idxint affine); #endif /* solve */ idxint ECOS_solve(pwork* w); /** * Cleanup: free memory (not used for embedded solvers, only standalone) * * Use the second argument to give the number of variables to NOT free. * This is useful if you want to use the result of the optimization without * copying over the arrays. One use case is the MEX interface, where we * do not want to free x,y,s,z (depending on the number of LHS). */ void ECOS_cleanup(pwork* w, idxint keepvars); /** * Version: returns the current version number * Use a character array of length 7 to obtain the version number * in the format * x.y.zzz * where x is the major, y the minor and zzz the build number */ const char* ECOS_ver(void); /* ------------------- EXPERT LEVEL INTERFACES ---------------------- */ /* * Updates one element of the RHS vector h of inequalities * After the call, w->h[idx] = value (but equilibrated) */ void ecos_updateDataEntry_h(pwork* w, idxint idx, pfloat value); /* * Updates one element of the OBJ vector c of inequalities * After the call, w->c[idx] = value (but equilibrated) */ void ecos_updateDataEntry_c(pwork* w, idxint idx, pfloat value); /* * Updates numerical data for G, A, c, h, and b, * and re-equilibrates. * Then updates the corresponding KKT entries. */ void ECOS_updateData(pwork *w, pfloat *Gpr, pfloat *Apr, pfloat* c, pfloat* h, pfloat* b); #ifdef __cplusplus } #endif #endif